All-Pay Auctions with Variable Rewards

We study all-pay auctions with variable rewards under incomplete information. In standard models, a reward depends on a bidder!s privately known type; however, in our model it is also a function of his bid. We show that in such models there is a potential for paradoxical behavior where a reduction in the rewards or an increase in costs may increase the expected sum of bids or alternatively the expected highest bidAll-Pay Auctions, Contests, R & D Races, Rent-Seeking.

Communication of Preferences in Contests for Contracts

This paper models a contest where several sellers compete for a contract with a single buyer. There are several styles of possible designs with a subset of them preferred by the buyer. We examine what happens when the buyer communicates information about his preferences. If the sellers are unable to change their style, then there is no effect on the welfare of the sellers. If the sellers are able to make adjustments, extra information may either boost or damage the sellers' profits. While the chance that there will be a proposal of a style preferred by the buyer cannot decrease, the buyer's surplus may increase or decrease.Contests, Procurement, Communication

The Optimal Design of Rewards in Contests

Using contests to generate innovation has and is widely used. Such contests often involve offering a prize that depends upon the accomplishment (effort). Using an all-pay auction as a model of a contest, we determine the optimal reward for inducing innovation. In a symmetric environment, we find that the reward should be set to c(x)/c′(x) where c is the cost of producing an innovation of level x. In an asymmetric environment with two firms, we find that it is optimal to set different rewards for each firm. There are cases where this can be replicated by a single reward that depends upon accomplishments of both contestants.contests; innovation; mechanism design

Which way to cooperate

Cooperation in real-world dilemmas takes many forms. We introduce a class of two-player games that permits two distinct ways to cooperate in the repeated game. One way to cooperate is to play cutoff strategies, which rely solely on a player's private value to defection. The second cooperative strategy is to take turns, which relies on publicly available information. Our initial experiments reveal that almost all cooperators adopt cutoff strategies. However, follow-up experiments in which the distribution of values to defection are made more similar show that all cooperators now take turns. Our results offer insight into what form a cooperative norm will take: for mundane tasks or where individuals otherwise have similar payoffs, taking turns is likely; for difficult tasks that differentiate individuals by skill or by preferences, cutoff cooperation will emerge.experimental economics; cooperation; incomplete information; alternating; cutoff strategies; random payoffs

It's My Turn ... Please, After You: An Experimental Study of Cooperation and Social Conventions

We introduce a class of two-player cooperation games where each player faces a binary decision, enter or exit. These games have a unique Nash equilibrium of entry. However, entry imposes a large enough negative externality on the other player such that the unique social optimum involves the player with the higher value to entry entering and the other player exiting. When the game is repeated and players' values to entry are private, cooperation admits the form of either taking turns entering or using a cutoff strategy and entering only for high private values of entry. Even with conditions that provide opportunities for unnoticed or non-punishable 'cheating', our empirical analysis including a simple strategy inference technique reveals that the Nash-equilibrium strategy is never the modal choice. In fact, most subjects employ the socially optimal symmetric cutoff strategy. These games capture the nature of cooperation in many economic and social situations such as bidding rings in auctions, competition for market share, labor supply decisions in the face of excess supply, queuing in line and courtship.cooperation, incomplete information, random payoffs, strategy inference, experimental economics.

A Note on Revenue Effects of Asymmetry in Private-Value Auctions

We formulate a way to study whether the asymmetry of buyers (in the sense of having different prior probability distributions of valuations) is helpful to the seller in private-value auctions (asked first by Cantillon [2001]). In our proposed formulation, this question corresponds to two important questions previously asked: Does a first-price auction have higher revenue than a second-price auction when buyers have asymmetric distributions (asked by Maskin and Riley[2000])? And does a seller enhance revenue by releasing information (asked by Milgrom and Weber[1982])? This is shown by constructing two Harsanyi games of incomplete information each having the same ex-ante distribution of valuations but in one beliefs are symmetric while in the other beliefs are sometimes asymmetric. Our main result is that answers to all three questions coincide when values are independent and are related when values are affiliated.Asymmetric Auctions; Asymmetric Beliefs; Affiliation; Linkage Principle

Multiple equilibria in asymmetric first-price auctions

Maskin and Riley (2003) and Lebrun (2006) prove that the Bayes-Nash equilibrium of �rst-price auctions is unique. This uniqueness requires the assumption that a buyer never bids above his value. We demonstrate that, in asymmetric �rst-price auctions (with or without a minimum bid), the relaxation of this assumption results in additional equilibria that are "substantial." Although in each of these additional equilibria no buyer wins with a bids above his value, the allocation of the object and the selling price may vary among the equilibria. Furthermore, we show that such phenomena can only occur under asymmetry in the distributions of values.Asymmetric auctions, �first-price auctions, multiple equilibria

Vote or Shout

We examine an environment with n voters each with a private value over two alternatives. We compare the social surplus of two mechanisms for deciding between them: majority voting and shouting. In majority voting, the choice with the most votes wins. With shouting, the voter who shouts the loudest (sends the costliest wasteful signal) chooses the outcome. We find that it is optimal to use voting in the case where n is large and value for each particular alternative of the voters is bounded. For other cases, the superior mechanism is depends upon the order statistics of the distribution of values.majority voting, voting procedures, social efficiency

Optimal Allocation without Transfer Payments

Often an organization or government must allocate goods without collecting payment in return. This may pose a difficult problem either when agents receiving those goods have private information in regards to their values or needs or when discriminating among agents using known differences is not a viable option. In this paper, we …nd an optimal mechnnism to allocate goods when the designer is benevolent. While the designer cannot charge agents, he can receive a costly but wasteful signal from them. We …nd conditions for which ignoring these costly signals by giving agents equal share (or using lotteries if the goods are indivisible) is optimal. In other cases, those that send the highest signal should receive the goods; however, we then show that there exist cases where more complicated mechanisms are superior. Finally, we show that the optimal mechanism is independent of the scarcity of the goods being allocated.mechanism design; efficient allocation; waiting lines; lotteries; all-pay auctions